Particulate matter is a pervasive constituent, ranging from droplets of fat in mayonnaise to boulders in an avalanche. Collections of many particles are considered to be a state of matter different from solids, liquids or gasses, distinguished by the existence of an amorphous and mechanically stable jammed state. Packing problems are ubiquitous, ranging from oil extraction through porous rocks to grain storage in silos and the compaction of pharmaceutical powders in tablets or capsules. At a given density, particulate systems pack into a mechanically stable and in cases into an amorphous state. Theoretical frameworks have proposed a connection between jamming and the glass transition, the thermodynamics of jamming and geometric modeling of random packings. Nevertheless, a simple underlying mechanism for the random assembly of athermal particles, analogous to crystalline ordering, remains unknown.